Sufficient conditions for spanning $k$-trees in tough graphs

Caili Jia, Yong Lu

The toughness of a graph $G$, denoted by $\tau (G)$, is defined by $\tau (G)=$min $\{\frac{|S|}{c(G-S)}:S\subseteq V(G)$ and $c(G-S)\ge 2\}$. A graph $G$ is said to be $\tau$-tough if $τ(G)\g…